CN112019348A - Smart phone cloud positioning method based on block chain privacy protection - Google Patents

Smart phone cloud positioning method based on block chain privacy protection Download PDF

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Publication number
CN112019348A
CN112019348A CN202010871951.1A CN202010871951A CN112019348A CN 112019348 A CN112019348 A CN 112019348A CN 202010871951 A CN202010871951 A CN 202010871951A CN 112019348 A CN112019348 A CN 112019348A
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mobile phone
phone user
service provider
information
user
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CN112019348B (en
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李磊
杜勋
卜晨阳
吴信东
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Hefei University of Technology
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Hefei University of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3263—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving certificates, e.g. public key certificate [PKC] or attribute certificate [AC]; Public key infrastructure [PKI] arrangements
    • H04L9/3268—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving certificates, e.g. public key certificate [PKC] or attribute certificate [AC]; Public key infrastructure [PKI] arrangements using certificate validation, registration, distribution or revocation, e.g. certificate revocation list [CRL]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/02—Protecting privacy or anonymity, e.g. protecting personally identifiable information [PII]

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Mobile Radio Communication Systems (AREA)
  • Telephonic Communication Services (AREA)

Abstract

The invention discloses a smart phone cloud positioning method based on block chain privacy protection, which comprises the following steps: 1. building a block chain network; 2. account registration/login stage and location information protection; 3. authorizing and canceling the authorization phase; 4. and (5) an information transmission stage. The invention can effectively prevent the position information of the mobile phone from being acquired by a position service provider at will, and simultaneously ensure the safe transmission of the position information of the mobile phone, thereby protecting the position privacy safety of mobile phone users.

Description

Smart phone cloud positioning method based on block chain privacy protection
Technical Field
The invention belongs to the technical field of data encryption and position privacy protection, and particularly relates to a smart phone cloud positioning method based on block chain privacy protection.
Background
With the rapid development of space positioning technology and mobile networks, the use form of the internet is also changed from fixed equipment such as 'PC' to mobile equipment such as smart phones, and the satellite navigation and location service industry is more rapidly developed. To date, Location Based Services (LBS) have been associated with people's lives. The location-based service is that a user obtains a geographical location of the user through a positioning technology of a mobile device such as a smart phone, and a location service provider provides various location services to the user according to the geographical location of the user. The location-based service greatly facilitates the life of people, but when the service is greatly facilitated, the position information of people is threatened to a certain degree.
At present, when a mobile phone user obtains self position information by an authorized position service provider, a set authorization strategy is rough. Common authorization policies today are permanent authorization and during-use authorization.
The permanent authorization is that once authorized, the location service provider can acquire the location information of the mobile phone user at any time and any place. However, when the mobile phone user does not need the location service, the location service provider can still obtain the location information of the mobile phone user by itself, and the location privacy of the mobile phone user is violated.
During-use authorization refers to allowing a location service provider to obtain location information of a mobile phone user when the user uses mobile phone software. During the use period, the authorization is improved to a certain extent compared with the permanent authorization, however, when the mobile phone application software still runs in the background, the location service provider can still obtain the location information of the mobile phone user, and the location privacy of the mobile phone user still cannot be reasonably protected. In addition, the authorized objects of the position information of the mobile phone user are relatively disordered, almost all software applications can initiate requests for acquiring the position information, and the position information of the mobile phone user can easily fall into the hands of illegal organizations by carelessness of the mobile phone user. Therefore, it is necessary to design an effective location privacy protection method to protect the location privacy of the mobile phone user.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a smart phone cloud positioning method based on block chain privacy protection, so that the position information of a mobile phone can be prevented from being randomly acquired by a position service provider, and meanwhile, the position is encrypted and transmitted, and the safety of the position privacy of a mobile phone user is ensured.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a smart phone cloud positioning method based on block chain privacy protection, which is characterized by comprising the following steps of:
step one, building a block chain network:
the block chain network is composed of at least 4 cloud servers, and the same account book data is arranged on all the cloud servers; enabling a cloud server to correspond to a mobile phone manufacturer;
each cloud server of each mobile phone manufacturer corresponds to a plurality of administrators, a plurality of mobile phone users and a plurality of location service providers; recording any one mobile phone user as u and recording a cloud server where the mobile phone user u is located as cs1Cloud server cs1Any administrator on is noted as m1(ii) a Recording any one location service provider as l, and recording a cloud server where the provider l is located as cs2Cloud server cs2Any administrator on is noted as m2；
The mobile phone manufacturer is responsible for the operation and maintenance of the block chain network, and manages the certificates of mobile phone users and location service providers through an administrator;
the mobile phone manufacturer generates an administrator certificate, an administrator account and public and private keys (PK _ M, SK _ M) of an administrator in advance;
each cloud server is provided with a node of a block chain, and the node comprises: ca node, Zookeeper node, Kafka node, Orderer node, Peer node;
the Ca node is responsible for providing certificate services;
the Zookeeper node and the Kafka node are responsible for realizing a cluster and consensus mechanism and enabling a blockchain network to normally operate when nodes of partial blockchains are down;
the Orderer node is responsible for packaging transactions and generating blocks;
the Peer node is used for deploying intelligent contracts and submitting transactions;
the mobile phone user accesses the block chain network through the SDK, submits the transaction and obtains a transaction result;
step two, account registration/login stage and position information protection:
step 2.1, manager m of mobile phone manufacturer1According to the unique identifier IMEI of the mobile phone user u, the cloud server cs1Initiating a certificate request for generating a mobile phone user u;
cloud server cs1Ca node on according to manager m1Generates a digital certificate of the mobile phone user u;
manager m2Using the name of location service provider l and other related information to cloud server cs2Initiating a certificate request for generating a supplier l;
cloud server cs2Ca node on according to manager m2Generates a digital certificate for location service provider l;
step 2.2, the mobile phone user U accesses the block chain network through the SDK to register a login account number, and obtains a secret key pair (PK _ U, SK _ U) comprising a public key and a private key;
the location service provider L accesses a block chain network through the SDK to register a login account number and obtains a secret key pair (PK _ L, SK _ L) comprising a public key and a private key;
step 2.3, the mobile phone user U uses the public key (PK _ U) to automatically encrypt the own location information msg, and obtains the encrypted location information C ═ EPK_U(msg); wherein E isPK_U() represents a cryptographic function;
step three, authorizing and canceling the authorization stage:
step 3.1, the location service provider l sends an information request for acquiring the location of the mobile phone to the mobile phone user u;
step 3.2, the mobile phone user u automatically calls a function for inquiring the user authorization list in the intelligent contract through the Peer node to inquire whether the related information of the location service provider l is in the authorization list of the mobile phone user;
if the user is in the authorization list, the mobile phone user u transmits the position information of the user to a position service provider l;
if the mobile phone is not in the authorization list, the mobile phone user u determines whether to authorize the location service provider l or not;
if the mobile phone user u agrees to authorize, the Peer node calls an authorization function in the intelligent contract to add the relevant information of the location service provider l to a user authorization list; meanwhile, the authorization policy of the location service provider l is determined by the mobile phone user u, so that the corresponding authorization policy is added to the authorization information of the location service provider l in the authorization list by calling an authorization policy function in the intelligent contract through the Peer node;
when the authorization policy made by the mobile phone user u for the location service provider l exceeds the condition set by the mobile phone user u, the Peer node automatically calls an authorization canceling function in the intelligent contract to remove the relevant information of the location service provider l from the authorization list of the mobile phone user u;
if the mobile phone user u does not agree with the authorization or the mobile phone user u does not respond within the specified time T, the location service provider l fails to acquire the location information of the mobile phone user u;
step four, information transmission stage:
step 4.1, the mobile phone user U decrypts the position information C by using its own private key (SK _ U) to obtain the position information msg ═ DSK_U(C) (ii) a Wherein D isSK_U() represents a decryption function;
step 4.2, the mobile phone user U firstly encrypts the position information msg by using the private key (SK _ U) of the mobile phone user U to obtain the information C after the first-stage encryption1＝ESK_U(msg) the first stage encrypted information C is then re-used with the public key of the location service provider L (PK _ L)1Encrypting to obtain the information C after the second stage of encryption2＝EPK_U(C1) Then the information C after the second stage of encryption is carried out2Is transmitted to the positionA service provider l; wherein E isSK_U() represents a cryptographic function; ePK_U() represents a cryptographic function;
step 4.3, the location service provider l receives the information C after the second stage of encryption2Then, the information C after the second stage encryption is carried out2Firstly, the private key (SK _ L) of the user is used for decryption to obtain the information C after the first-stage encryption1＝DSK_L(C2) Then, the public key (PK _ U) of the mobile phone user U is used for encrypting the information C after the first stage1Decrypting to obtain the position information msg ═ D of the mobile phone user uPK_U(C1) (ii) a The location service provider l provides corresponding location service to the mobile phone user u according to the location information msg; wherein D isSK_L() represents a decryption function; dPK_U(. cndot.) represents an encryption function.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention ensures that the identity of the authorized object of the mobile phone user is reliable by issuing the digital certificate to the position service provider and compiling the intelligent contract function, simultaneously, the authorization strategy becomes more accurate and flexible, and the security of the position privacy of the mobile phone user is improved.
2. According to the invention, the Ca node in the block chain network is used for endorsement of the position service provider and issuing the corresponding digital certificate, so that the reliability of the identity of the position service provider is ensured; meanwhile, only the location service provider who issues the digital certificate and joins the block chain network can request the mobile phone user to carry out location authorization, so that the authorization objects of the mobile phone user are ensured to be reliable, and the possibility that an illegal organization obtains the location information of the mobile phone user is low.
3. The invention encrypts the mobile phone position information by the public key obtained after the registration of the mobile phone user, ensures the safety of the mobile phone position information to a certain extent, and is difficult to decrypt to obtain accurate mobile phone position information even if the mobile phone position information is illegally obtained without the private key of the mobile phone user.
4. The invention formulates the position authorization strategy as much as possible for the mobile phone user by compiling the intelligent contract function, and the mobile phone user inputs corresponding parameters during authorization, so that the position authorization strategy of the mobile phone user is more accurate and flexible compared with the prior art.
5. The method manages the authorization of the mobile phone user by compiling the intelligent contract function, and when the authorization strategy made by a certain user u for a certain position service provider l exceeds the condition set by the mobile phone user u, the intelligent contract function automatically triggers the authorization information of the position service provider l to be removed from the authorization list of the mobile phone user u; therefore, the position service provider is difficult to acquire the position information of the mobile phone user wantonly.
6. The invention adopts the public and private keys generated when the mobile phone user and the position service provider are registered to encrypt and decrypt the position information during transmission, thereby ensuring the transmission safety of the position information.
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FIG. 1 is an overall architecture diagram of the present invention;
fig. 2 is a diagram of the network architecture of the present invention.
Detailed Description
In this embodiment, a smart phone cloud positioning method based on block chain privacy protection is performed according to the following steps:
step one, building a block chain network:
the specific overall architecture is shown in fig. 1: firstly, a mobile phone manufacturer is characterized by being responsible for the operation and maintenance of a block chain network, and managing certificates of mobile phone users and position service providers through a configuration administrator; the mobile phone user is characterized in that the mobile phone user is authorized to a position service provider and allows the position service provider to obtain self position information; the position service provider is characterized in that position service is provided for the mobile phone user according to the position information of the mobile phone user; block chain network, the network architecture is shown in fig. 2.
The block chain network is composed of at least 4 cloud servers, and the same account book data is arranged on all the cloud servers; enabling a cloud server to correspond to a mobile phone manufacturer;
each cloud server is provided with block chain link points, and the method comprises the following steps: ca node, Zookeeper node, Kafka node, Orderer node, Peer node;
the Ca node is responsible for providing certificate services;
the Zookeeper node and the Kafka node are responsible for realizing a cluster and consensus mechanism and enabling a blockchain network to normally operate when nodes of partial blockchains are down;
the Orderer node is responsible for packaging transactions and generating blocks;
the Peer node is used for deploying an intelligent contract function and submitting a transaction; the intelligent contract function refers to a piece of code deployed on a Peer node, and when a specified condition is extracted and satisfied, the corresponding intelligent contract function automatically calls execution.
Table 1 is an intelligent contract function table;
function name Description information Caller
createAdmin Registration manager Administrator
loginAdmin Administrator login Administrator
addUser Administrator added certificate Administrator
getAdmin Administrator inquiry certificate Administrator
deleteUser Administrator deletion certificate Administrator
loginUser User login Mobile phone user, position service provider
createUser Registering a user Mobile phone user, position service provider
getAuthorizationInfo Query authorization information Mobile phone user
addAuthorization Adding authorization Mobile phone user
removeAuthorization Deleting authorization Mobile phone user
timeAuthorization Time authorization Mobile phone user
frequencyAuthorization Frequency grant Mobile phone user
The intelligent contract functions deployed on all Peer nodes are shown in Table 1; in this embodiment, the mobile phone user has two kinds of time authorization function and frequency authorization function for the authorization policy function of the location service provider. the parameter of the timeAuthorization function is the time length authorized by the user; the frequency authorization function frequency authorization parameter is the number of times that the mobile phone user allows the location service provider to acquire the mobile phone location information; in addition, other intelligent contract authorization functions can be formulated;
a mobile phone user accesses a block chain network through the SDK, submits a transaction and obtains a transaction result;
each cloud server where each mobile phone manufacturer is located corresponds to a plurality of administrators, a plurality of mobile phone users and a plurality of location service providers; recording any one mobile phone user as u and the cloud server where the mobile phone user u is located as cs1Cloud server cs1M is any administrator on1(ii) a Let any one location service provider be l, and the cloud server where provider l is located be cs2Cloud server cs2M is any administrator on2；
A mobile phone manufacturer calls a createAdmin function in an intelligent contract to generate an administrator certificate, an administrator account and public and private keys (PK _ M, SK _ M) of an administrator in advance; the generated public key is usually public, the public key is encrypted, and the private key is decrypted; the private key encrypts and the public key decrypts.
Step two, account registration/login stage and position information protection:
step 2.1, manager m of mobile phone manufacturer1Calling an addUser function in an intelligent contract to a cloud server cs according to the unique identifier IMEI of the mobile phone user u1Initiating a certificate request for generating a mobile phone user u;
cloud server cs1Ca node on according to manager m1Generates a digital certificate of the mobile phone user u;
manager m2Calling addUser function in intelligent contract to cloud server cs by using name of location service provider l and other related information2Initiating a certificate request for generating a supplier l;
cloud server cs2Ca node on according to manager m2Generates a digital certificate for location service provider l;
step 2.2, the mobile phone user U accesses the block chain network through the SDK, a createUser function in the intelligent contract is called to register a login account, and a secret key pair (PK _ U, SK _ U) comprising a public key and a private key is obtained;
a location service provider L accesses a block chain network through the SDK, calls a createUser function in an intelligent contract to register a login account number, and obtains a secret key pair (PK _ L, SK _ L) comprising a public key and a private key;
step 2.3, the mobile phone user U uses the public key (PK _ U) to automatically encrypt the own location information msg, and obtains the encrypted location information C ═ EPK_U(msg); wherein E isPK_U() represents a cryptographic function;
the mobile phone user u encrypts the position information by using the public key thereof, wherein the position information is encrypted information C even if the position information is leaked;
step three, authorizing and canceling the authorization stage:
step 3.1, the location service provider l sends an information request for acquiring the location of the mobile phone to the mobile phone user u;
step 3.2, the mobile phone user u automatically calls an authorization information query function getAuuthorizationInfo in the intelligent contract through the Peer node to query whether the related information of the location service provider l is in the authorization list of the mobile phone user u;
if the user is in the authorization list, the mobile phone user u transmits the position information of the user to a position service provider l;
if the mobile phone is not in the authorization list, the mobile phone user u determines whether to authorize the location service provider l or not;
if the mobile phone user u agrees to authorize, the Peer node calls an authorization function in the intelligent contract to add the relevant information of the location service provider l into a user authorization list; meanwhile, the mobile phone user u determines that the authorization strategy of the location service provider l is frequency authorization and the frequency of the authorization is appointed to be 3 times, so that the frequency authorization function frequency authorization in the intelligent contract is called by the Peer node to add the authorization strategy to the authorization information of the location service provider l in the authorization list;
the authorization frequency means that the number of times that the location service provider l can obtain the location information of the mobile phone user u is 3 times under the authorization;
when the number of times that the position service provider acquires the position information of the mobile phone user u reaches 3 times, the Peer node automatically calls a delete authorization function in the intelligent contract to remove the relevant information of the position service provider l from an authorization list of the mobile phone user u;
if the mobile phone user u does not agree with the authorization or the mobile phone user u does not respond within the specified time T, the location service provider l fails to acquire the location information of the mobile phone user u;
step four, information transmission stage:
step 4.1, the mobile phone user U decrypts the position information C by using its own private key (SK _ U) to obtain the position information msg ═ DSK_U(C) (ii) a Wherein D isSK_U() represents a decryption function;
since the information amount of the location information is small, the public and private keys of the user u and the location service provider l are used for directly performing encryption transmission.
Step 4.2, the mobile phone user U firstly encrypts the position information msg by using the private key (SK _ U) of the mobile phone user U to obtain the information C after the first-stage encryption1＝ESK_U(msg) the first stage encrypted information C is then re-used with the public key of the location service provider L (PK _ L)1Encrypting to obtain the information C after the second stage of encryption2＝EPK_U(C1) Then the information C after the second stage of encryption is carried out2Transmitting to location service provider l; wherein E isSK_U() represents a cryptographic function; ePK_U() represents a cryptographic function;
step 4.3, location service provider l receives information C2Then, for the information C2Firstly, the private key (SK _ L) of the user is used for decryption to obtain the information C1＝DSK_L(C2) Then, the public key (PK _ U) of the mobile phone user U is used for pairing the information C1Decrypting to obtain the position information msg ═ D of the mobile phone user uPK_U(C1) (ii) a Therefore, the location service provider l provides corresponding location service for the mobile phone user u according to the location information msg; wherein D isSK_L() represents a decryption function; dPK_U(. cndot.) represents an encryption function.

Claims (1)

1. A smart phone cloud positioning method based on block chain privacy protection is characterized by comprising the following steps:
step one, building a block chain network:
the block chain network is composed of at least 4 cloud servers, and the same account book data is arranged on all the cloud servers; enabling a cloud server to correspond to a mobile phone manufacturer;
each cloud server of each mobile phone manufacturer corresponds to a plurality of administrators, a plurality of mobile phone users and a plurality of location service providers; recording any one mobile phone user as u and recording a cloud server where the mobile phone user u is located as cs1Cloud server cs1Any administrator on is noted as m1(ii) a Recording any one location service provider as l, and recording a cloud server where the provider l is located as cs2Cloud server cs2Any administrator on is noted as m2；
The mobile phone manufacturer is responsible for the operation and maintenance of the block chain network, and manages the certificates of mobile phone users and location service providers through an administrator;
the mobile phone manufacturer generates an administrator certificate, an administrator account and public and private keys (PK _ M, SK _ M) of an administrator in advance;
each cloud server is provided with a node of a block chain, and the node comprises: ca node, Zookeeper node, Kafka node, Orderer node, Peer node;
the Ca node is responsible for providing certificate services;
the Zookeeper node and the Kafka node are responsible for realizing a cluster and consensus mechanism and enabling a blockchain network to normally operate when nodes of partial blockchains are down;
the Orderer node is responsible for packaging transactions and generating blocks;
the Peer node is used for deploying intelligent contracts and submitting transactions;
the mobile phone user accesses the block chain network through the SDK, submits the transaction and obtains a transaction result;
step two, account registration/login stage and position information protection:
step 2.1, manager m of mobile phone manufacturer1According to the unique identifier IMEI of the mobile phone user u, the cloud server cs1Initiating a certificate request for generating a mobile phone user u;
cloud server cs1Ca node on according to manager m1Generates a digital certificate of the mobile phone user u;
manager m2Using the name of location service provider l and other related information to cloud server cs2Initiating a certificate request for generating a supplier l;
cloud server cs2Ca node on according to manager m2Generates a digital certificate for location service provider l;
step 2.2, the mobile phone user U accesses the block chain network through the SDK to register a login account number, and obtains a secret key pair (PK _ U, SK _ U) comprising a public key and a private key;
the location service provider L accesses a block chain network through the SDK to register a login account number and obtains a secret key pair (PK _ L, SK _ L) comprising a public key and a private key;
step 2.3, the mobile phone user U uses the public key (PK _ U) of the user to automatically encrypt the position information msg of the user to obtainTo the encrypted position information C ═ EPK_U(msg); wherein E isPK_U() represents a cryptographic function;
step three, authorizing and canceling the authorization stage:
step 3.1, the location service provider l sends an information request for acquiring the location of the mobile phone to the mobile phone user u;
step 3.2, the mobile phone user u automatically calls a function for inquiring the user authorization list in the intelligent contract through the Peer node to inquire whether the related information of the location service provider l is in the authorization list of the mobile phone user;
if the user is in the authorization list, the mobile phone user u transmits the position information of the user to a position service provider l;
if the mobile phone is not in the authorization list, the mobile phone user u determines whether to authorize the location service provider l or not;
if the mobile phone user u agrees to authorize, the Peer node calls an authorization function in the intelligent contract to add the relevant information of the location service provider l to a user authorization list; meanwhile, the authorization policy of the location service provider l is determined by the mobile phone user u, so that the corresponding authorization policy is added to the authorization information of the location service provider l in the authorization list by calling an authorization policy function in the intelligent contract through the Peer node;
when the authorization policy made by the mobile phone user u for the location service provider l exceeds the condition set by the mobile phone user u, the Peer node automatically calls an authorization canceling function in the intelligent contract to remove the relevant information of the location service provider l from the authorization list of the mobile phone user u;
if the mobile phone user u does not agree with the authorization or the mobile phone user u does not respond within the specified time T, the location service provider l fails to acquire the location information of the mobile phone user u;
step four, information transmission stage:
step 4.1, the mobile phone user U decrypts the position information C by using its own private key (SK _ U) to obtain the position information msg ═ DSK_U(C) (ii) a Wherein D isSK_U() represents a decryption function;
step 4.2, mobile phone user uFirstly, the position information msg is encrypted by the private key (SK _ U) of the user to obtain information C after the first-stage encryption1＝ESK_U(msg) the first stage encrypted information C is then re-used with the public key of the location service provider L (PK _ L)1Encrypting to obtain the information C after the second stage of encryption2＝EPK_U(C1) Then the information C after the second stage of encryption is carried out2Transmitting to the location service provider; wherein E isSK_U() represents a cryptographic function; ePK_U() represents a cryptographic function;
step 4.3, the location service provider l receives the information C after the second stage of encryption2Then, the information C after the second stage encryption is carried out2Firstly, the private key (SK _ L) of the user is used for decryption to obtain the information C after the first-stage encryption1＝DSK_L(C2) Then, the public key (PK _ U) of the mobile phone user U is used for encrypting the information C after the first stage1Decrypting to obtain the position information msg ═ D of the mobile phone user uPK_U(C1) (ii) a The location service provider l provides corresponding location service to the mobile phone user u according to the location information msg; wherein D isSK_L() represents a decryption function; dPK_U(. cndot.) represents an encryption function.
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